Variable selection for joint mean and dispersion models of the inverse Gaussian distribution

Abstract

The choice of distribution is often made on the basis of how well the data appear to be fitted by the distribution. The inverse Gaussian distribution is one of the basic models for describing positively skewed data which arise in a variety of applications. In this paper, the problem of interest is simultaneously parameter estimation and variable selection for joint mean and dispersion models of the inverse Gaussian distribution. We propose a unified procedure which can simultaneously select significant variables in mean and dispersion model. With appropriate selection of the tuning parameters, we establish the consistency of this procedure and the oracle property of the regularized estimators. Simulation studies and a real example are used to illustrate the proposed methodologies.

Variable selection of varying dispersion student-t regression models

“…All the simulation results are summarized in Tables 1 and 2 with SCAD penalty and LASSO penalty, respectively. As in Wu and Li [5] , Zhao and Xue [21] , the performance of estimators β and γ will be assessed by using generalized mean square error (GMSE), defined as In the tables, Column "C" shows the average number of zero coefficients correctly estimated to be zero, and Column "IC" presents the average number of nonzero coefficients incorrectly estimated to be zero over 1000 simulations. In the column labeled "Under-fit", we present the proportion of excluding any nonzero coefficients in 1000 replications.…”

“…Automatic selection of the tuning parameters λ 1j and λ 2k using data-driven methods is desirable and yet computationally expensive because one has to search over an r-dimensional grid for the proposed penalized estimator. To save computation cost, we follow the strategy of Wang, et al [20] and Wu and Li [5] , setting…”

“…Based on Score function (5) and Hessian matrix (6) or Fisher information matrix (7), we can update the estimate of θ for VDTRM with fixed freedom degree v (k) at (k + 1)-th iteration, i.e.,…”

“…Taylor and Verbyla [4] proposed joint modelling of location and dispersion parameters for Student-t linear regression. For inverse Gaussian distribution, Wu and Li [5] studied the joint mean and dispersion models of the inverse Gaussian regression model. Recently, Wu, et al [6] discussed the joint location and scale models of the skew-normal distribution.…”

Bayesian Subset Selection for Inverse Gauss Regression Models

“…Xu et al [7] developed a Bayesian procedure to analyze the double generalized linear regression models of the inverse Gaussian distribution. Wu and Li [8] employed penalized likelihood function approach to simultaneously select significant variables in mean and dispersion models of the inverse Gaussian distribution.…”